HDU

6647

比赛的时候， 用了一种垃圾树hash，没过去。。

#pragma GCC optimize(2)
#pragma GCC optimize(3)
#include<bits/stdc++.h>
#define LL long long
#define LD long double
#define ull unsigned long long
#define fi first
#define se second
#define mk make_pair
#define PLL pair<LL, LL>
#define PLI pair<LL, int>
#define PII pair<int, int>
#define SZ(x) ((int)x.size())
#define ALL(x) (x).begin(), (x).end()
#define fio ios::sync_with_stdio(false); cin.tie(0);

#define ll long long
using namespace std;

const int N = 1e5 + 7;
const int inf = 0x3f3f3f3f;
const LL INF = 0x3f3f3f3f3f3f3f3f;
const int mod = 998244353;
const double eps = 1e-8;
const double PI = acos(-1);

template<class T, class S> inline void add(T &a, S b) {a += b; if(a >= mod) a -= mod;}
template<class T, class S> inline void sub(T &a, S b) {a -= b; if(a < 0) a += mod;}
template<class T, class S> inline bool chkmax(T &a, S b) {return a < b ? a = b, true : false;}
template<class T, class S> inline bool chkmin(T &a, S b) {return a > b ? a = b, true : false;}

mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());

const ull B = 1000000007;

int n, m, p, id[N];
int F[N], Finv[N], inv[N];
int way[N], totway[N];
ull sz[N];
ull hsson[N];
ull hstot[N];
ull Pow[N];
ull rnd[N];

int Rt = 1;

int depth[N];

vector<pair<ull, int>> V[N];
vector<int> G[N];

void dfs(int u, int fa) {
    way[u] = 1;
    hsson[u] = 0;
    sz[u] = 1;
    depth[u] = depth[fa] + 1;

    for(int i = 0; i < SZ(G[u]); i++) {
        if(G[u][i] == fa) {
            G[u].erase(G[u].begin() + i);
            break;
        }
    }

    for(auto &v : G[u]) {
        dfs(v, u);
        V[u].push_back(mk(hsson[v], v));
        way[u] = 1LL * way[u] * way[v] % mod;
        sz[u] += sz[v];
    }

    sort(ALL(V[u]));
    for(auto &t : V[u]) {
        hsson[u] = hsson[u] * Pow[sz[t.se]] + t.fi;
    }

    hsson[u] = hsson[u] * B + rnd[sz[u]];

    way[u] = 1LL * way[u] * F[SZ(V[u])] % mod;

    for(int i = 0, j = 0; i < SZ(V[u]); i = j) {
        while(j < SZ(V[u]) && V[u][j].fi == V[u][i].fi) j++;
        way[u] = 1LL * way[u] * Finv[j - i] % mod;
    }
}

void dfs2(int u, ull fhs, int fway) {
    int divway = 1;
    int mulway = 1;
    if(u != Rt) {
        V[u].push_back(mk(fhs, 0));
    }
    for(int i = SZ(V[u]) - 1; i > 0; i--) {
        if(V[u][i] < V[u][i - 1]) swap(V[u][i], V[u][i - 1]);
    }
    hstot[u] = 0;
    totway[u] = 1;
    for(auto &t : V[u]) {
        if(t.se) {
            totway[u] = 1LL * totway[u] * way[t.se] % mod;
            hstot[u] = hstot[u] * Pow[sz[t.se]] + t.fi;
        }
        else {
            totway[u] = 1LL * totway[u] * fway % mod;
            hstot[u] = hstot[u] * Pow[n - sz[u]] + t.fi;
        }
    }

    totway[u] = 1LL * totway[u] * F[SZ(V[u])] % mod;
    hstot[u] = hstot[u] * B + rnd[n];


    vector<int> cnt(SZ(V[u]));

    for(int i = 0, j = 0; i < SZ(V[u]); i = j) {
        while(j < SZ(V[u]) && V[u][j].fi == V[u][i].fi) j++;
        totway[u] = 1LL * totway[u] * Finv[j - i] % mod;
        divway = 1LL * divway * Finv[j - i] % mod;
        for(int k = i; k < j; k++) {
            cnt[k] = j - i;
        }
    }

    mulway = F[SZ(V[u]) - 1];

    vector<pair<ull, int>> pre(SZ(V[u]));
    vector<pair<ull, int>> suf(SZ(V[u]));
    vector<int> sufsz(SZ(V[u]) + 1, 0);

    ull tmphs = 0;
    int tmpway = 1;
    int tmpsz = 0;

    for(int i = 0; i < SZ(V[u]); i++) {
        if(V[u][i].se) {
            tmpway = 1LL * tmpway * way[V[u][i].se] % mod;
            tmphs = tmphs * Pow[sz[V[u][i].se]] + V[u][i].fi;
        }
        else {
            tmpway = 1LL * tmpway * fway % mod;
            tmphs = tmphs * Pow[n - sz[u]] + V[u][i].fi;
        }
        pre[i] = mk(tmphs, tmpway);
    }

    tmphs = 0;
    tmpway = 1;
    tmpsz = 0;

    for(int i = SZ(V[u]) - 1; i >= 0; i--) {
        if(V[u][i].se) {
            tmpway = 1LL * tmpway * way[V[u][i].se] % mod;
            tmphs += Pow[tmpsz] * V[u][i].fi;
            tmpsz += sz[V[u][i].se];
        }
        else {
            tmpway = 1LL * tmpway * fway % mod;
            tmphs += Pow[tmpsz] * V[u][i].fi;
            tmpsz += n - sz[u];
        }
        suf[i] = mk(tmphs, tmpway);
        sufsz[i] = tmpsz;
    }

    for(int i = 0; i < SZ(V[u]); i++) {
        if(V[u][i].se == 0) continue;
        tmphs = 0, tmpway = 1;
        if(i + 1 < SZ(V[u])) {
            tmphs = suf[i + 1].fi;
            tmpway = 1LL * tmpway * suf[i + 1].se % mod;
        }
        if(i) {
            tmphs += pre[i - 1].fi * Pow[sufsz[i + 1]];
            tmpway = 1LL * tmpway * pre[i - 1].se % mod;
        }
        tmphs = tmphs * B + rnd[n - sz[V[u][i].se]];
        tmpway = 1LL * tmpway * mulway % mod;
        tmpway = 1LL * tmpway * divway % mod;
        tmpway = 1LL * tmpway * F[cnt[i]] % mod;
        tmpway = 1LL * tmpway * Finv[cnt[i] - 1] % mod;
        dfs2(V[u][i].se, tmphs, tmpway);
    }
}

void init() {
    for(int i = 1; i <= n; i++) {
        G[i].clear();
        V[i].clear();
    }
}

int main() {
    F[0] = Finv[0] = inv[1] = Pow[0] = 1;
    for(int i = 1; i < N; i++) {
        Pow[i] = Pow[i - 1] * B;
    }
    for(int i = 2; i < N; i++) {
        inv[i] = 1LL * (mod - mod / i) * inv[mod % i] % mod;
    }
    for(int i = 1; i < N; i++) {
        F[i] = 1LL * F[i - 1] * i % mod;
    }
    for(int i = 1; i < N; i++) {
        Finv[i] = 1LL * Finv[i - 1] * inv[i] % mod;
    }
    for(int i = 1; i < N; i++) {
        rnd[i] = rng();
    }
    int T; scanf("%d", &T);
    while(T--) {
        scanf("%d", &n);
        init();
        for(int i = 1; i <= n; i++) {
            id[i] = i;
        }
        for(int i = 1; i < n; i++) {
            int u, v;
            scanf("%d%d", &u, &v);
            G[u].push_back(v);
            G[v].push_back(u);
        }

        dfs(Rt, 0);
        dfs2(Rt, 0, 1);

        sort(id + 1, id + 1 + n, [&](int A, int B) {
            return hstot[A] < hstot[B];
        });

        int ans = 0;
        for(int i = 1; i <= n; i++) {
            if(i == 1 || hstot[id[i]] != hstot[id[i - 1]]) {
                add(ans, totway[id[i]]);
            }
        }
        printf("%d
", ans);
    }
    return 0;
}

/*
*/